It wasn't until the 1960's that women started to enter the workforce by massive numbers, and women started building sports leagues and participating in sports that had always been considered male activities. There were smaller attemps prior the 1960's, but not many women felt liberated or independent enough to participate. So we men have a few centuries of a headstart when it comes to sports.
According to David Epstein, writer of "The Sports Gene", given enough time, women will eventually dominate most sports that men have traditionally dominated throughout history. Of course, physical sports such as football or UFC is unlikely, due to the physical differences between average men and average women. But all other sports that require strategy, agility, nerves, hand-eye coordination, or a combination of any of these things will certainly be up for grabs. I'm in favor of having men and women compete more with each other, move away from all-men or all-women leagues for thise who would really like to open up the gates of competition.